If the US is assumed to be at war with Germany and Britain et al., are still actively fighting even after the British Isles are occupied, then the US remains a viable threat to Germany. One can assume in such a case the US would have made Japan the primary target and defeated that nation by late 1944 or early 1945. The following are also reasonable assumptions based on historical data:

The US would have continued to expand their military into 1945 having as many as 200+ divisions available. The US Navy would be the same gigantic force it originally was meaning that Germany is essentially powerless to stop an Atlantic crossing or inflict any meaningful casualties on such an operation using seapower. The US would also have sufficent carrier forces by that point to reasonably challenge what Luftwaffe forces might be present.
The Germans would be far less aware of US intentions and operations than the Allies would be of German dispositions. Germany had no spy network in the US while one can reasonably expect a large and active one in German occupied nations.
With a very reduced convoy / shipping escort requirement the Allies can likely sweep the Atlantic of U-boats using ASW groups and aircraft. The Germans would be forced to operate much further from their bases rendering alot of their U-boats worthless (ie the Type VIIs) as these lack the range to operate off the US or outside the eastern north Atlantic.
The Germans would also certainly get hit with nuclear bombs at some point. This would likely be another rude shock far beyond some of the ones like use of Window or H2S were. Since Japan would almost certainly fall before nuclear weapons were available the surprise would be complete. The US could have used a B-36 or B-29 out of Iceland to deliver such a weapon. It is very unlikely that Germany could mount an invasion of this island given its defenses which would, no doubt, have been beefed up following the fall of Britain. It is simply that the Germans lack naval power and the amphibious capacity to carry out such an operation.

Another problem for the Germans is that the Allies could begin their own "U-boat" campaign against German shipping, such as it was. This could cause serious problems supplying their forces in Britain. Again, the lack of naval power by Germany is going to be a severe handicap to their challenging Allied naval operations.....And, the Luftwaffe is no substitute.

On that last, let's just say the US shows up with a 5 to 7 division amphibious assault with say 200+ warships in tow. If we assume the Luftwaffe has say, 200 to 300 aircraft in Britain immediately available for use how long would they last? I would speculate based on US operations off Okinawa that the Germans would lose air superiority within a week after which they could mount the occasional strike with substancial losses. Off Okinawa the Japanese threw almost 5000 aircraft (mostly in suicide missions) against the US barely making a dent in their naval operations.
A couple hundred aircraft not trained in anti-shipping operations could hardly be expected to do much at all.

The problem here for the Germans is that fighting a war in an occupied Britain is first and foremost a naval operation something they are virtually incapable of sustaining.